Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the first partial derivative with respect to x
Find the first partial derivative with respect to y
gx=−x6
Evaluate
g(x,y)=y−ln(x×1)×6
Simplify
More Steps
Evaluate
y−ln(x×1)×6
Any expression multiplied by 1 remains the same
y−ln(x)×6
Multiply the terms
y−6ln(x)
g(x,y)=y−6ln(x)
Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x
gx=∂x∂(y−6ln(x))
Use differentiation rule ∂x∂(f(x)±g(x))=∂x∂(f(x))±∂x∂(g(x))
gx=∂x∂(y)−∂x∂(6ln(x))
Use ∂x∂(c)=0 to find derivative
gx=0−∂x∂(6ln(x))
Evaluate
More Steps
Evaluate
∂x∂(6ln(x))
Use differentiation rule ∂x∂(f(x)×g(x))=∂x∂(f(x))×g(x)+f(x)×∂x∂(g(x))
∂x∂(6)×ln(x)+6×∂x∂(ln(x))
Evaluate
0×ln(x)+6×∂x∂(ln(x))
Evaluate
0+6×∂x∂(ln(x))
Use ∂x∂lnx=x1 to find derivative
0+6×x1
Evaluate
0+x6
Removing 0 doesn't change the value,so remove it from the expression
x6
gx=0−x6
Solution
gx=−x6
Show Solution
